Alice Cooper is unusual in music circles in that both the man and the band had two different but equally influential primary influences - music and film/TV. It's that mix that made them so unique. From almost the beginning they saw the potential of using theatrics and props as part of their rock show, and while they obviously weren't the first to ever do it they took theatrics in rock much further then anyone previously, and in turn influenced almost every live act to follow them in some way, whether they realise it or not, via the trickle down effect. Nowadays it's not that unusual to see some new pop sensation on TV using one of the Cooper's old tricks, be it Madonna and the electric chair, or Britney Spears using the snake or magic screen.

Musically the band had the normal influences similar bands had in the late 60s - Elvis, Chuck Berry and the original Rock'n'rollers, then The Beatles and The Stones - but they were arguably more influenced by two British acts - The Who and, especially, The Yardbirds. To this day Alice still names The Yardbirds as his favourite band. Of course there were many more in the mix (Love, The Doors/Jim Morrison, Pink Floyd, Beach Boys etc).

Many people over the years have brought up both Arthur Brown and Screaming Lord Sutch as obvious influences. As far as Sutch is concerned it's a highly unlikely the Cooper's had ever heard of him. While it's true that he was doing the horror image thing well before Alice Cooper, he was barely known outside of the UK and parts of Europe. Even with that Screaming Jay Hawkins pre-dated Sutch with similar horror shtick, and he was American, so if it had come from anywhere it would have more likely been there.
Brown is a slightly different story. The band had certainly played a few festivals with him in the late 60s, although whether they actually saw his act is unknown. Alice has stated he may have heard 'Fire' at some point and have been aware of the flaming headdress Brown used, but that was about it until much later. There are also photographs of Brown wearing similar make up to the classic Alice look. It's certainly possible that there was an influence but unlikely it was conscious. The band was full of their own ideas at the time and it's unlikely they would have simply copied something they knew someone else as already doing in such a way.

Alice wrote a short article naming specific songs as influences on what he did:

  1. Chuck Berry: "Sweet Little Sixteen"
    It was the first record I bought which really got to me. I mean, when I first heard it I thought I was imagining it - I couldn't believe a record could be so exciting. I still love it now - to me, Berry is the best lyricist of all time. If the guy couldn't think of a word, he'd invent one. Don't give me no botheration.' Ha ha! That's brilliant!
  2. Elvis Presley: "Hound Dog"
    This is the record which changed my life. I was six at the time and when I heard it, it opened me up to rock'n'roll. I realised then that the lyrics didn't have to make any sense for the record to affect you. As soon as I heard that song, I changed my hairstyle: I got myself a quiff. I guess I must have looked a pretty strange six-year-old kid, huh?"
  3. The Beach Boys: "I Get Around"
    They were such a band. They were the classic white pop band before The Beatles started making their mark in the States, and this song's still in a league of its own. I remember my family and I were living in Arizona at the time, and this song made even people living in the desert try to find somewhere to surf. It was the archetypal youth song. It mentioned everything a teenager ever wanted - cars, girls, hanging out with your buddies... what a wonderful world.
  4. The Beatles: "She Loves You"
    This record made me change my hair again. From a slicked-back Elvis quiff to a bowl haircut overnight. Like 'I Get Around', this said so much to teenagers about their life. When I heard this, it was like being struck by lightning. I was stunned: I walked around the house in a daze.
  5. The Rolling Stones: "It's All Over Now"
    As you can imagine, my parents didn't take too kindly to me walking round the house with a bowl haircut, so they absolutely hated The Beatles. That all changed when they heard the Stones. They loved The Beatles after that. As far as they were concerned, anything was preferable to the Stones, who were just dirty punks. Needless to say, like any teenager I figured what annoyed my parents was fine with me. I remember thinking that, when I started a band, I wanted to make the Stones look like saints.
  6. The Kinks: "You Really Got Me"
    It was the sound of the guitar that hit me. I'd never heard anything like it before. Someone told me Jimmy Page played it, not Ray Davies, but I don't know if that's true [it isn't]. Still, the song is so cool. It was all jittery, and that riff was so sharp, I was blown away.
  7. The Yardbirds: 'Rave On'
    This album became the most played record of my youth. Aerosmith would say the same - any guys who were 15 and at high school when the British Invasion happened will cite all those bands like The Kinks, the Stones and The Yardbirds as the soundtrack to their teen rebellion. It was these records which made us decide to be in rock'n'roll bands, so we all grew our hair real long and got thrown out of school. Being from Detroit, I was never a Motown fan - a song had to have a guitar riff for me to care about it - and hearing Jeff Beck play in The Yardbirds was the ultimate guitar experience for me for many, many years.
  8. The Beach Boys: "Pet Sounds"/The Beatles: "Sgt. Pepper's Lonely Heart's Club Band"
    I've chosen The Beach Boys and The Beatles again, but they sounded like different bands by the time they made these albums. There's so much going on on 'Pet Sounds'. It advanced recording techniques beyond any known limits and, although 'Sgt. Pepper' copied that, it still had a style of its own. 'Pet Sounds' was a very American album, 'Sgt. Pepper' was much more exotic and mysterious. Brian Wilson invited me and Iggy over to his house one day, and he took us down to his basement and there was this 72-track tape of 'Pet Sounds' set up. He turned to us and said, 'Want to mix it.' We just looked at him blankly and he said, 'Go ahead, mix it the way you want to hear it.' So there's me and Iggy playing around for six hours with these tapes, and Iggy kept shouting, 'Turn the guitars up, man!' It was wild. Should they have released our version. What do you think?
  9. Pink Floyd: "Piper At The Gates Of Dawn"
    So far, all these records have been an influence. The rest are records I love dearly. When this came out, my band played it to death, to death, to death... the original line-up lived with us for a while in Los Angeles. It was a - uh - weird time, I guess. Syd Barrett didn't speak for a fortnight. Good record, though.
  10. The Doors: "Strange Days"
    I used to think that, when you know people in bands, you knew the real person behind the stage persona. That all went out of the window when we met The Doors. We got to know them pretty well in LA - and, you know, Jim Morrison was really like that. He passionately believed all that Dionysian stuff. The lesson I learnt from him was that you can't live the rock'n'roll lifestyle for very long. It's just not designed that way. Look at people like him, Keith Moon and Janis Joplin - they all thought they could carry on forever. Strange, though - it's often people like that, people on the edge, who make the greatest records.
  11. John Barry: "Goldfinger"
    Yeah, yeah, laugh if you like, but Barry has a brilliant grasp of sound. We were all big movie fans, so, to us, people like John Barry were as much stars as The Beatles or the Stones. There's a great moment in this film where fighter planes dive bomb a factory, and Barry adds this great, sweeping orchestration to the scene. It made me think, 'Wow, I wonder if we can do that with guitars?' - so we tried it on 'Billion Dollar Babies'.

That last choice is a telling one. John Barry was famous for his soundtrack music, especially his work on the James Bond films of which the band were big fans. They even wrote 'The Man With The Golden Gun' for 'Muscle Of Love' in an attempt to get it used on the forthcoming Bond film. Then there's the Bond--esque parts of 'Halo Of Flies' from 'Killer' or 'Unfinished Sweet' from 'Billion Dollar Babies'. Barry was a huge influence, at least as much if not more that the more rock orientated acts.

Another early nonmusical influence came from their association with Frank Zappa, or more precisely his band of groupies The GTOs. Alice was dating Miss Christine and all the band spent a lot of time around the GTOs in the last 60s. At least two books give credit to them for the early Alice Cooper look, but that would really be overstating it, and especially disregarding the input of Cindy Smith (Later Cindy Dunaway), who was already making many of the clothes the band were seen in. Cindy's influence in terms of their look should never be underestimated as she was there from the beginning and all through the years they slowly worked their way to the top. It was Cindy's love of sparkle and sequins that started the whole Glam Rock movement in the early seventies. Much of what bands like Sweet, David Bowie, Slade and T-Rex wore in 1972 the Cooper's had already been used by the Coopers several years before.

Also worth mentioning, certainly in terms of stage production, is Busby Berkeley, and to a lesser degree the 'Zeigfeld Follies' shows.
Berkeley was a film director and dance choreographer who made his name through his use of large numbers of show girls, props and fantasy elements, including the famous kaleidoscopic top-down shots of multiple dancers, in his on screen dance routines in the 1930s to 1950s. Rolling Stone even ran a lengthy article on the band called 'Gold Diggers of 1984', a direct reference to Busby Berkeley's 'Gold Diggers of ...' series of films in the 1930s. In fact, one stage setting for 'Gold Diggers of 1933' featured similar light up steps to the ones used in the 'Billion Dollar Babies' show.
The 'Zeigfeld Follies' were a series of extravagant Broadway musical revues which were inspired by the 'Folies Bergére' in Paris. While the band would have never seen the original productions there were several films based on them, notably the 1964 MGM production called 'Zeigfeld Follies' which stared Fred Astaire, Judy Garland, Lena Horne, William Powell, Gene Kelly and many others (note many of those names are included on the 'Greatest Hits' cover illustration).

To these you can also add 'Hellzapoppin', a 1941 Universal Pictures film based on a Broadway musical of the same name. In interviews Alice has mentioned the name more than once as a big influence. The previously mentioned 'Lady Is A Tramp' sequence could be a lift from the film, which opens with a song and dance number in hell that is eventually revealed to be a movie set, just like the opening sequence in 'Good To See You Again, Alice Cooper'. In fact the whole opening sequence of 'Hellzapoppin' comes across as a little Cooper-esque to me. It even includes a few chickens!

While these were all almost certainly influential, it was of course more in terms of staging then musically. In fact film musicals in general, and 'West Side Story' in particular, were certainly an influence - just look at the skeleton dance sequence in the 'Welcome To My Nightmare' show (also influenced by Disney 1929 short 'The Skeleton Dance'?), or 'The Lady Is A Tramp' from 'Good To See You Again, Alice Cooper'. It's pure Broadway and closer to 'Singing In The Rain' then 'My Generation'.